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 ChebyshevT

 http://functions.wolfram.com/07.04.21.0006.01

 Input Form

 Integrate[ChebyshevT[\[Nu], z], \[Nu]] == (Sqrt[1 - z^2] ChebyshevU[\[Nu] - 1, z])/ArcCos[z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], RowBox[List["\[DifferentialD]", "\[Nu]"]]]]]], "\[Equal]", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", " ", "-", " ", SuperscriptBox["z", RowBox[List[" ", "2"]]]]]], RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "z"]], "]"]]]], RowBox[List["ArcCos", "[", "z", "]"]]]]]]]

 MathML Form

 T ν ( z ) ν 1 - z 2 cos - 1 ( z ) U ν - 1 ( z ) ν ChebyshevT ν z 1 -1 z 2 1 2 z -1 ChebyshevU ν -1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["ChebyshevT", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], RowBox[List["\[DifferentialD]", "\[Nu]_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]], " ", RowBox[List["ChebyshevU", "[", RowBox[List[RowBox[List["\[Nu]", "-", "1"]], ",", "z"]], "]"]]]], RowBox[List["ArcCos", "[", "z", "]"]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2001-10-29